I usually turn one of my business problems into a case interview style question.
I often used this method in Product Management interviews and have adapted it to suit almost any level and role of employee.
Anyone smart has a rehearsed answer to open ended personality questions or prepared "intelligent" questions about my business. It's best to shake things up.
Using a real business situation keeps people from feeling like they're being interviewed, putting them at ease and allows me to evaluate their ability and interest to work through a challenge.
Here's an example: Some people that visit our site go directly to the pricing page and leave. How do we make sure they read more of the home page content first or convert them to customers from pricing?